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If Rob or Mike Sigman see this thread perhaps they could contribute more, but it's an interesting question where the Yoseikan Budo founder's son learned this movement, and what differences there may be in the Yoseikan world.

Dan, there's a certain logic to this stuff that's difficult to go outside of, once you're in it. Trying quickly to think of some analogy that will allow me to toss in a meaningful but short comment, let me try this:

Imagine one of those snap-together flexible support-poles that form the outside through-the-loops structure of many lightweight portable tents nowadays. About 9-feet long, I guess. If you line that pole up against an incoming force correctly, you can keep the incoming force at a distance.... but consider that only a "pole skill" used to strengthen the pole and not something you would really do as a strategy or technique. That example is the equivalent of pretty much all of Tohei's and Ueshiba's "withstand a push" demonstrations that they did. They formed flexible "poles" throughout their body, starting from the ground, at their will.

Now take that same pole and put against, I dunno, a wall. You want to shake a wave pulse down that pole while simultaneously timing a push straight down the pole so that the combined forces of the push and the wave arrive together for maximum power. You can see a couple of problems, I'm sure, but the main problem is that if you concentrate too much on "making a wave" and neglect to keep the tip of the pole against the wall (or aimed at it), you'll blow the objective. A "wave" that is not focused along a connected, flexible, a focused path will simply be a "wave" (as cool as it sounds) and won't be particularly powerful. To do it correctly takes a path from the ground, a trained connection, and a wave-path that is focused along the path from the ground to the target. You can't just think "I'll hit him with a wave and that will knock his socks off"... it takes some knowledge (usually needs to be shown) and some training. And yeah, variations of this skill are found in a great number of Asian martial arts, but in my experience, that's a reasonable general description.

The wave movement I've seen, is when you really break it down, simply an open/close of the major joints of the body(Btw, anyone in the know, don't shoot me, this is a huge huge oversimplification ). You can parody the skill in certain ways and this is probably why a lot of people missed the mark in gaining these skills.
Case in point, the shotokan hipsnap, certain systema guys thinking just waving the chest produces KO power etc...

When someone with a body that's conditioned in the manner that's been discussed in previous threads, the "open/close" of the major joints (namely the scaps and pelvic girdle) can create tremendous power. This open/close of certain joints can be likened to waving, but it can also be a "shake", a "tremble", "vibration" etc. That's not even adding in other elements like slamming the diaphram/koshi area down into your foot etc.

Anyways, Ark shows plenty of "wave" like demonstrations of how to use the body. He often says, once you have the right "body", most of this stuff will come naturally. First thing to do is to condition the body so it becomes connected. Then you can start to talk power generation.

The way I describe it to my students is using the idea of popping someone with a towel. If you don't pull back slightly at the end, you get no pop, pull back slightly as the towel's tip is almost extended and you accelerate the tip of the towel.

This is the same for the punch, this slight pull back while the fist is still going forward gives tremendous acceleration and focuses the energy in a tighter pattern.

I've always had a problem with likening the wave/snap motion to a towel or whip. It just doesn't make sense to me, though I don't have the physics knowledge to outright disprove it.

Basically, the human arm or leg simply isn't as flexible as a towel or whip, so I don't see how a human limb can transfer energy in the same way. Furthermore, the power of a towel/whip comes from the "flicking" motion. But you don't really "flick" punches and kicks, you drive them straight. You can "flick" a backhand, and some kicks, but "normal" punches and kicks are "straight" (at least, the ones I used to practice in karate were).

Also, the way I understand whips (and to a lessor extent towels), the reason the wave accelerates is because the whip tapers from handle to tip. Energy is conserved, thus the motion accelerates as the mass of the whip decreases. The human body isn't built this way. Furthermore, a whip can get moving really, really fast. The "crack" of the whip comes from the tip moving faster than the speed of sound, a mini-sonic boom. The human body certainly can't do that.

I'm sure there are other "wave"-like actions the human body can make, but I don't see how they can be the same as a towel or whip.

Basically, the human arm or leg simply isn't as flexible as a towel or whip, so I don't see how a human limb can transfer energy in the same way. Furthermore, the power of a towel/whip comes from the "flicking" motion.
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Yes, the human body in most cases is not as flexible as the towel or whip. However, the wave or kinetic chain would seem to me to be generated from the center outward if transfering energy or inward if grounding energy. To make that happen would only require relaxed connection, grounding and the ability to vibrate, pulse, or whatever you want to call it, one's center.

Also, the way I understand whips (and to a lessor extent towels), the reason the wave accelerates is because the whip tapers from handle to tip. Energy is conserved, thus the motion accelerates as the mass of the whip decreases. The human body isn't built this way. Furthermore, a whip can get moving really, really fast. The "crack" of the whip comes from the tip moving faster than the speed of sound, a mini-sonic boom. The human body certainly can't do that.

As in many incremental analyses, you can have several perspectives and analyse a particular phenomenon in terms of forces, levers, momentum, momentum transfer, Impulse, and so on.

What you're saying about a whip is that as you shake a wave down the braided body of the whip, the decrease in diameter of the whip means that velocity must increase as the mass of the whip decreases, because M1V1 = m2v2 (the momentum of a particular mass and velocity must be conserved). Then you say that the human body isn't really built this way, which is true..... but in a way, the body is sort of built like this.

The equation M1V1 = m2v2 can be looked at as the basic explanation of why a billiard ball can roll into another billiard ball and the first ball stops while the second ball begins rolling away. If we make the mass (M1) of the first ball to be twice the mass of the second ball, then the second ball (in a perfect, inelastic collision, neglecting friction, etc.) will wind up rolling away at twice the velocity the first ball arrived with. In a lot of ways, you can look at the torso/middle of our body as the larger first ball and the arm/fist as the smaller second ball. The same transfer of momentum can happen if you connect things up correctly.

Better yet, make it 3 balls. The earth is the first ball, the torso/tanden is the second ball, the arm/fist would be the third ball.

If you re-read my post, I acknowledged that wave-like actions were possible. It's the whip analogy I have difficulty accepting.

Mike, I get idea of "pulsing" from your center into the hand. But I have some honest questions:

When you "pulse" from the center, does the power/energy travel from the body down the arm to the hand? Or is the entire movement a coordinated, simultaneous action? What I mean is, back in my karate days, I would snap my hips, then a split-second later the power/energy would transfer to my arm and my hand would start moving.

After you, err... "pulse outward" with your center, do you actively "retract"? Back in my karate days---and earlier in this thread---it was advised that one should pull the hand or foot backwards after the strike. (There's a certain tactical advantage to this, but it's hard for me to see how it contributes to power generation.)

When you "pulse" from the center, does the power/energy travel from the body down the arm to the hand? Or is the entire movement a coordinated, simultaneous action? What I mean is, back in my karate days, I would snap my hips, then a split-second later the power/energy would transfer to my arm and my hand would start moving.

Well, to cut to the chase and to keep it focused, let me just try to reiterate my perhaps poorly-made point: A "wave" or "towel snap" can pop someone, but it's not really all that powerful unless it is supported by something akin to that rod I mentioned in the other post. That "rod" can represent the path from the hands to the ground that someone like Tohei, O-Sensei, and others demonstrates when they show they are "immoveable", etc. An empty wave isn't all that powerful; a wave riding along a supporting path is powerful as an assist. You don't really need a wave in most cases, if you can store power along that path, bear in mind.

If you use a "wave", you're obviously doing what is called "sequential movement". The thing about sequential movement is that it's more or less what a whip does and one factor has to be in common.... if the "connection" between all the segments isn't good, the power is lost. If you snap your hips and then you only trigger off the hip snap, you haven't done much. If your body connection is good, the hip snap actually does the work and the torque across the torso will throw the arm out. That's the difference between actually using the center to strike and triggered sequential movement.

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After you, err... "pulse outward" with your center, do you actively "retract"? Back in my karate days---and earlier in this thread---it was advised that one should pull the hand or foot backwards after the strike. (There's a certain tactical advantage to this, but it's hard for me to see how it contributes to power generation.)

Depends. It's a discussion about Impulse. If I want to hurt someone, I tend to make the contact very short and very sharp. If I just want to bounce someone back for a demo, I maintain contact much longer so that it becomes simply a momentum transfer.

After you, err... "pulse outward" with your center, do you actively "retract"? Back in my karate days---and earlier in this thread---it was advised that one should pull the hand or foot backwards after the strike. (There's a certain tactical advantage to this, but it's hard for me to see how it contributes to power generation.)

To build on what Mike said, if you have two balls of equal mass, ball one is stationary, the ball two rolls into ball one with a given "speed", then under ideal conditions, ball two will stop, and ball one will roll away with the speed ball two had. Basically, the speed lost by ball two, equals the speed gained by ball one. So if we add some spin, and we make ball two bounce back after the collision, then the change in speed from positive x to negative y, is larger, hence ball one, will now have a speed equal to x+y.

Hence the snap back increases the change in momentum. The force of the strike is then given by the change in momentum, divided by the time the strike occurs over. Hence a quick snap back, also increases the force.

This is the opposite principle behind an air bag in a car, which increase the time, decreasing the force.

The equation M1V1 = m2v2 can be looked at as the basic explanation of why a billiard ball can roll into another billiard ball and the first ball stops while the second ball begins rolling away. If we make the mass (M1) of the first ball to be twice the mass of the second ball, then the second ball (in a perfect, inelastic collision, neglecting friction, etc.) will wind up rolling away at twice the velocity the first ball arrived with.

I *think* you mean 'elastic collision' rather than inelastic. An elastic collision preserves the most kinetic energy by conserving all of it. I was bored a while ago, so I did the math on this. It doesn't really change your point, but it's a detail that's worth considering if one starts really thinking about what can happen:

If the first ball is twice the mass of the second ball, then actually (in an elastic collision) the second ball will only roll away at 1 1/3 the speed the first ball started with. This is because in order for kinetic energy to be conserved, the first ball has to continue rolling at 1/3 of its original speed. Once the first ball's mass exceeds the second ball's, it is not possible for it to transfer all of its momentum. The reason this is possible with pool balls is because they each have the same mass.

The best you can do with an elastic collision is for the second ball to leave with double the speed the first ball arrived at -- but this is the theoretical limit as the ratio of the masses approaches infinity. For example, if the first ball is 100 times heavier than the second, the second ball leaves at 1.98 times the original speed.

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In a lot of ways, you can look at the torso/middle of our body as the larger first ball and the arm/fist as the smaller second ball. The same transfer of momentum can happen if you connect things up correctly.

And the above analysis points out that the proportionally bigger the first ball, the closer you can come to getting double the velocity out of the second ball. However, that's the best you can do. So once you've gotten those proportions worked out, the only way (within this formula) to add more kinetic energy to the second ball is to increase the velocity of the first ball. You can only go so far by increasing mass (to the first ball; increasing mass of the whole system will always help, but any increase in mass of the second ball needs to be proportionally matched in the first ball in order not to slip back in terms of velocity transfer). All else being the same, the faster you can get the first ball going, the faster the second ball will go.

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Better yet, make it 3 balls. The earth is the first ball, the torso/tanden is the second ball, the arm/fist would be the third ball.

But of course you cannot actually get the earth moving. What you *can* do is take advantage of its mass to accelerate the second ball by knocking it off the first ball. In an elastic collision, this won't actually buy you anything. However, if you are adding power to the ball over time, it gives you a longer path over which to accelerate the middle ball (more work = more energy). Better still, if you can make the collision with the ground be 'super-elastic' then the impact itself will effectively add energy. The only way to accomplish that is for some form of stored energy to be brought into play. If you imagine colliding with the sprung part of a mousetrap, you can see that you might be able to leave the collision with more energy than you entered with. Of course this only works if someone else put the energy there by setting the mousetrap in the first place.

I know *you* know this Mike, more clearly I am sure than I do. I just threw it out there for the number geeks to chew on. If my math's wrong, please point it out -- but I think I got the equations right.

No, I was using a lossless example in order to simplify the illustration. An elastic collision adds more factors and is not good for simple examples.

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An elastic collision preserves the most kinetic energy by conserving all of it. I was bored a while ago, so I did the math on this. It doesn't really change your point, but it's a detail that's worth considering if one starts really thinking about what can happen:

If the first ball is twice the mass of the second ball, then actually (in an elastic collision) the second ball will only roll away at 1 1/3 the speed the first ball started with. This is because in order for kinetic energy to be conserved, the first ball has to continue rolling at 1/3 of its original speed. Once the first ball's mass exceeds the second ball's, it is not possible for it to transfer all of its momentum. The reason this is possible with pool balls is because they each have the same mass.

The best you can do with an elastic collision is for the second ball to leave with double the speed the first ball arrived at -- but this is the theoretical limit as the ratio of the masses approaches infinity. For example, if the first ball is 100 times heavier than the second, the second ball leaves at 1.98 times the original speed.

And the above analysis points out that the proportionally bigger the first ball, the closer you can come to getting double the velocity out of the second ball. However, that's the best you can do. So once you've gotten those proportions worked out, the only way (within this formula) to add more kinetic energy to the second ball is to increase the velocity of the first ball. You can only go so far by increasing mass (to the first ball; increasing mass of the whole system will always help, but any increase in mass of the second ball needs to be proportionally matched in the first ball in order not to slip back in terms of velocity transfer). All else being the same, the faster you can get the first ball going, the faster the second ball will go.

But of course you cannot actually get the earth moving. What you *can* do is take advantage of its mass to accelerate the second ball by knocking it off the first ball. In an elastic collision, this won't actually buy you anything. However, if you are adding power to the ball over time, it gives you a longer path over which to accelerate the middle ball (more work = more energy). Better still, if you can make the collision with the ground be 'super-elastic' then the impact itself will effectively add energy. The only way to accomplish that is for some form of stored energy to be brought into play. If you imagine colliding with the sprung part of a mousetrap, you can see that you might be able to leave the collision with more energy than you entered with. Of course this only works if someone else put the energy there by setting the mousetrap in the first place.

I know *you* know this Mike, more clearly I am sure than I do. I just threw it out there for the number geeks to chew on. If my math's wrong, please point it out -- but I think I got the equations right.

I was only trying to say what time it was; not how to build a watch, CK.

I'm going first to go back to the wave, or the whip, analogy for explaining the power generation in Hiroo Mochizuki's pedagogy.

The wave has an inverse relationship between amplitude and frequency.
A large wave has a large amplitude and a low frequency. It is visible.
A short wave is the opposite. It is almost not visible.

Visible, here, means that you have the time to understand what you are seeing because of the slow speed and the large amplitude motion.
Invisible means that you don't have the time to understand the images because of the high speed and very low amplitude motion.

So, H.Mochizuki starts with the large wave so as to facilitate the demo of what body parts exactly are moving, and how momentum is transmitted through the whole body.

There is a specific sequential body coordination in order to produce ascending or descending waves in the sagittal and frontal planes.
Both direction waves can also be combined into one cyclic "wheel motion" (circling up/down or down/up) in any plane.

The large wave can be applied in combat, particularly for the throws.
The short waves are more used for atemi, and for weapons manipulation.

The short wave isn't no more really a "wave", as it can't be visually seen like that (you can't see a clear waving, with up and down curves travelling, in alternance, through the body).
H. Mochizuki calls then it a "vibration".
But this explosive motion is supposed to be the same pattern as the "undulation".

Frequency is very high and amplitude is very low, thus the eyes only see a kind of shaking, or a vibration of the whole body.
It all seems to appear in simultaneity, rather like a sequencial motion because of the high speed.

For the purpose of pedagogy, the large undulation can be exercized very slowly, so as to let the time to the body awareness to be impressed (awareness is rather limited).
It means that under these special exercices conditions, you can really follow what is moving and how.

But of course, for combat application, be it as a sequencial motion (imagine an explosive Judo throw for example), or as a quasi-(or true) simultaneous motion, the wave becomes very quick, hence a vibration.

I personally think that the wave analogy in Yoseikan Budo has to be carefully explained in order to clarify what "sequencial" and what "simultaneous" words actually mean.

When considering the fact that a body wave has some amplitude (meaning that it contains "dynamic ups and downs" travelling through the body), it is then very important to understand that the "down body parts" are NOT totally relaxed, like being completely passively waiting for the momentum.
[Please, excuse my poor language!]

Yes, there is some degree of "passivity" in order to let the primary impulse coordinate the whole body parts.
But the whole body is still actively maintaining an aligned structure (tonic function), that is going to be further dynamized by the impulse.
Only then, the impulse can be precisely channeled (axially) to the intended contact point.

If you represent the whole body as a dynamic alignement of several blocks (tensional blocks, not compressive blocks), you can visualize what exactly is this body wave.
And you can understand why the use of the whip or the wave analogy.

You can see the body as composed by 3 general articulated blocks:
- legs
- trunk/head
- arms

The "central block" is that one of the trunk/head, and it is there that originates the primary impulse.
The trunk itself can sub-divided into 5 components:
- the pelvis
- the abdomino-lumbar
- the thorax
- the head
- and the full spine

Thanks to this simplified, yet precisely articulated, body model, you can initiate a very precise body wave.
And also, you can see that by initiating only one trunk impulse, it is going to immediately affect the whole trunk/head dynamic alignement.

It can't be truly a "sequential motion", because if you move one "block" (by closing/opening), it is the whole spine (and other blocks) that undulates altogether.

The critical element is then the coordination (and timing) of this impulse through the various "body blocks".
Essentially, it means that there is NOT fixed center of motion, and that periphery is as much important for re-cycling the momentum (fourth/back).

Once there is a primary impulse, you have to make it continuously "alive" (if you want), by re-cycling it like in a closed circuit.
This re-cycling of momentum is particularly critical thanks to the spine.

For example, there is no relaxed chest wave possible without a corresponding head wave, a corresponding abdomino-lumbar wave, and a corresponding pelvic wave.
However, it is possible to make a big chest wave but simultaneously "freeze" the head wave at the top...
Momentum is then stopped at the top.

Stopping the momentum is NOT a problem if you can maintain the aligned structure.
Potential motion is still available at will.
You then simply release the "body blocks", as if motion was just beeing kept in "suspension" at the top (or in "compression" at the bottom if this is the case), waiting for this release.
The important element is the wave itself motion between these two polarities.

Solar plexus is the center of the closing/opening of the trunk (between abdomino-lumbar/thorax which corresponds to vertebra T8):
- this dynamic center allows the belly to be "full" and the chest to be "empty".

But this solar plexus center has to be synchronized with each extremities of the bow, the pelvis and the head.
Only then, the spine can function like a bow (compression/extension).
Even turning is possible without a thoracic vertebra rotation, but only just cervical rotation.
It is just a closing/opening of the trunk around the solar plexus/T8 into a diagonal.
But it requires some trunk mobility and relaxation.
It also requires a different pattern coordination than the usual.

Finally, I agree with many who have said that the wave model is not new, nor unique to Hiroo Mochizuki. Others have discovered it as well.
At the same time, each one method is specific, and so Yoseikan Budo has its unique savour.
I, for example, palso articularly appreciate the Kenji Tokitsu's method (Tokitsu Ryu), and the Kajo Tsuboi 's method (Kiryuho), among others.

Dan, there's a certain logic to this stuff that's difficult to go outside of, once you're in it. ... Imagine one of those snap-together flexible support-poles that form the outside through-the-loops structure of many lightweight portable tents nowadays. ... That example is the equivalent of pretty much all of Tohei's and Ueshiba's "withstand a push" demonstrations that they did. They formed flexible "poles" throughout their body, starting from the ground, at their will. ...

There are other ways of thinking about it, too, however. Waves are quintessential examples of conservation of angular momentum as somewhat divorced from the structures or medium in which they operate -- i.e. the energy travels globally, while the medium moves only locally, minimally and cyclically. This is an aspect of wave/particle nonduality at the macroscale.

While very simple in operation, it can be very spooky because the the actual cause of movement is relatively difficult to percieve, and the ultimate effect of the movement is highly unforeseen. Tsunamis are devastatingly huge, but they lift the surface of the ocean only a few inches and then drop it down again, hardly above background noise -- but coordinated with a totality of interaciton that is difficult to envision -- the total circulation system of the tsunami is from surface to the bottom and many, many miles long. The vortex energy in the water wave is cyclic and rotating, but the individual components of the medium simply go up slightly and then down again as the massive energy passes leaving them each barely disturbed.

Poles in the analogy operate as sprung structures, i.e. -- depending on material torsional or tensile strength as with mechanical springs (taking as a given that no one is pushing hard enough to crush bones in compression).

Sprung structures will vibrate in compression waves easily enough, but not in ways that concentrate kinetic energy in geometric terms as with a loosely bound snapping whip or flailing chain. Likewise, sprung structures do not as easily dissipate kinetic energy as with the attempt to push on a chain. The physical concept of vorticity and the Chinese "open/close" of joints are not that dissimilar in their understanding of the manipulation of this form of energy -- positively or negatively.

For Rob: the vibration shaking or trembling is just higher frequencies of waves particularly at the end of the limbs or the weapon where the positively applied rotational energy is constantly reducing in radius -- thus decreasing in wavelength and increasing frequency and geometrically increasing in total impulse when finally meeting the target. There are two squared energy terms in the relevant equations. In examples of fajin, which is very much given as example s on these topics, the whip model is precisely accurate, and for Tim -- some of the videos of that actually do show the result in the gentleman's cuffs snapping just like the end of the whip.

The whip or flail is the image of the positive concentration model -- the negative model is really best seen in aerodynamic lift, or in destabilized arches. Both are directly applicable also here. If you consider the joints or limb elements as individual whorls of briefly rotating energy, and adaptive in their "viscosity" or relative pliability under impulse, the way it works on the negative phase becomes more clear. Ellis Amdur's very persuasive argument that O Snesei's purpose in "editing" waza from DTR was in selecting those whose ukemi required opening and softening of joints fits this set of observations very closely. Lewis Richardson's doggerel poem is the among the best summaries of the dissipative principle:

Big whorls have little whorls
Which feed on their velocity,
And little whorls have lesser whorls
And so on to viscosity.

Grounding in one manner stores energy in the sprung structure, as Mike suggests. Grounding in another way, merely reflects the wave off the ground like a wave reflects off the beach -- One can generate waves as well as receive them, and thus the thing that can be controlled is the phase of generated wave, or that that the ground reflects, relative to the phase that is being received. I am not saying that grounded energy is not useful or applicable -- but it is not the whole story either - the Ki of Heaven is as just as useful as the Ki of Earth.

Like waves reflecting off the beach, if they meet the oncoming swells with peaks coinciding, the energy doubles and the oncoming wave's energy becomes unstable and breaks and falls down chaotically, or if the reflected trough coincides with the oncoming peak the energy literally vanishes at that point. No grounding required, and at no time do the energies collide or create resistance in the medium they are traversing, (they literally pass through one another), while at the same time causing interesting effects in the medium (bodily structure, in our case) at the point where they are meeting.

The largest energies may require this reflected grounding to avoid injury to weaker structures, but smaller energies may be reflected from any other suitable joint by meeting it with a negative or positive counter-phase, which in one phase is physically equivalent to meeting a barrier like the ground, or in the other phase, like falling into a hole. The body can be manipulate to control the phase delay to dissipate progressively, to transmit without much dissipation, or to alter the phase and magnitude in or joining with and transmitting it

The way in which the joints are addressed to the wave phase they are receiving/generating is another aspect of the "quantizing" of the angular momentum energy in a continuous/discontinuous form that I perceive to operate also in proper control of ma-ai, which I mentioned before.

The only significant difference is that ma-ai involves considering the connected person and oneself as one medium, and the fact that two minds may be involved in the interaction. In a sense, by attacking you give up your receptive mind (ukemi) in proportion to your commitment to the strike and thus only one mind may actually be operating in full possession of its senses at the moment of contact -- as O Sensei's numerous comments about attacking suggest.

Conversely, applied energy can also be eaten up in rotational inertia at each link in the chain if the body's joints are disposed correctly to receive the energy in dissipation. It can even be redirected back into the source along the yin line of the incoming wave going back the other way at the exact point of contact, although this is the most difficult and most highly trained manner of doing this.

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A "wave" that is not focused along a connected, flexible, a focused path will simply be a "wave" (as cool as it sounds) and won't be particularly powerful.

No arguments -- action must occur with awareness and sensitivity.

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Mike Sigman wrote:

To do it correctly takes a path from the ground, a trained connection, and a wave-path that is focused along the path from the ground to the target.

All except that grounding (in my sense of the term) is one way, not the only way. Several ways of applying angular momentum in the chain or whip model (tekubi furi undo as the chief example) actually "unground" the body and literally lift its weight with the applied acceleration UPWARD vice downward to ground -- making it more easily and speedily moved at a moment of critical contact WHILE applying energy into the target -- and not merely as a secondary reaction to that energy. The same can be applied in connection to the other person's body, either floating or grounding them depending -- if they are not able to make the necessary adjustments in turn .

The most critical application for utilizing the upward Ki pulse that enables swifter movement -- is with the sword. Both suri-age, and kiri-age, (upward and downward vertical sweeping cuts) can be performed so as to either lift or ground the body at several critical junctures in the movement, depending on the situation. The "vibrational" finish seen in ken suburi in Saito's curriculum makes this action somewhat visible.

It basically depends on whether you catch the applied angular momentum travelling down the body on the down cycle or the up cycle when you gird the undercarriage -- one lifts -- the other grounds. All of this has to be intuitive in action, although the reasons for doing one or the other depending on what is happening are perfectly capable of being analyzed to improve training.

I'm going first to go back to the wave, or the whip, analogy for explaining the power generation in Hiroo Mochizuki's pedagogy.

The wave has an inverse relationship between amplitude and frequency.
A large wave has a large amplitude and a low frequency. It is visible.
A short wave is the opposite. It is almost not visible.

Visible, here, means that you have the time to understand what you are seeing because of the slow speed and the large amplitude motion.
Invisible means that you don't have the time to understand the images because of the high speed and very low amplitude motion.

So, H.Mochizuki starts with the large wave so as to facilitate the demo of what body parts exactly are moving, and how momentum is transmitted through the whole body.

There is a specific sequential body coordination in order to produce ascending or descending waves in the sagittal and frontal planes.
Both direction waves can also be combined into one cyclic "wheel motion" (circling up/down or down/up) in any plane.

The large wave can be applied in combat, particularly for the throws.
The short waves are more used for atemi, and for weapons manipulation.

The short wave isn't no more really a "wave", as it can't be visually seen like that (you can't see a clear waving, with up and down curves travelling, in alternance, through the body).
H. Mochizuki calls then it a "vibration".
But this explosive motion is supposed to be the same pattern as the "undulation".

Frequency is very high and amplitude is very low, thus the eyes only see a kind of shaking, or a vibration of the whole body.
It all seems to appear in simultaneity, rather like a sequencial motion because of the high speed.

For the purpose of pedagogy, the large undulation can be exercized very slowly, so as to let the time to the body awareness to be impressed (awareness is rather limited).
It means that under these special exercices conditions, you can really follow what is moving and how.

But of course, for combat application, be it as a sequencial motion (imagine an explosive Judo throw for example), or as a quasi-(or true) simultaneous motion, the wave becomes very quick, hence a vibration.

I personally think that the wave analogy in Yoseikan Budo has to be carefully explained in order to clarify what "sequencial" and what "simultaneous" words actually mean.

When considering the fact that a body wave has some amplitude (meaning that it contains "dynamic ups and downs" travelling through the body), it is then very important to understand that the "down body parts" are NOT totally relaxed, like being completely passively waiting for the momentum.
[Please, excuse my poor language!]

Yes, there is some degree of "passivity" in order to let the primary impulse coordinate the whole body parts.
But the whole body is still actively maintaining an aligned structure (tonic function), that is going to be further dynamized by the impulse.
Only then, the impulse can be precisely channeled (axially) to the intended contact point.

If you represent the whole body as a dynamic alignement of several blocks (tensional blocks, not compressive blocks), you can visualize what exactly is this body wave.
And you can understand why the use of the whip or the wave analogy.

You can see the body as composed by 3 general articulated blocks:
- legs
- trunk/head
- arms

The "central block" is that one of the trunk/head, and it is there that originates the primary impulse.
The trunk itself can sub-divided into 5 components:
- the pelvis
- the abdomino-lumbar
- the thorax
- the head
- and the full spine

Thanks to this simplified, yet precisely articulated, body model, you can initiate a very precise body wave.
And also, you can see that by initiating only one trunk impulse, it is going to immediately affect the whole trunk/head dynamic alignement.

It can't be truly a "sequential motion", because if you move one "block" (by closing/opening), it is the whole spine (and other blocks) that undulates altogether.

The critical element is then the coordination (and timing) of this impulse through the various "body blocks".
Essentially, it means that there is NOT fixed center of motion, and that periphery is as much important for re-cycling the momentum (fourth/back).

Once there is a primary impulse, you have to make it continuously "alive" (if you want), by re-cycling it like in a closed circuit.
This re-cycling of momentum is particularly critical thanks to the spine.

For example, there is no relaxed chest wave possible without a corresponding head wave, a corresponding abdomino-lumbar wave, and a corresponding pelvic wave.
However, it is possible to make a big chest wave but simultaneously "freeze" the head wave at the top...
Momentum is then stopped at the top.

Stopping the momentum is NOT a problem if you can maintain the aligned structure.
Potential motion is still available at will.
You then simply release the "body blocks", as if motion was just beeing kept in "suspension" at the top (or in "compression" at the bottom if this is the case), waiting for this release.
The important element is the wave itself motion between these two polarities.

Solar plexus is the center of the closing/opening of the trunk (between abdomino-lumbar/thorax which corresponds to vertebra T8):
- this dynamic center allows the belly to be "full" and the chest to be "empty".

But this solar plexus center has to be synchronized with each extremities of the bow, the pelvis and the head.
Only then, the spine can function like a bow (compression/extension).
Even turning is possible without a thoracic vertebra rotation, but only just cervical rotation.
It is just a closing/opening of the trunk around the solar plexus/T8 into a diagonal.
But it requires some trunk mobility and relaxation.
It also requires a different pattern coordination than the usual.

Finally, I agree with many who have said that the wave model is not new, nor unique to Hiroo Mochizuki. Others have discovered it as well.
At the same time, each one method is specific, and so Yoseikan Budo has its unique savour.
I, for example, palso articularly appreciate the Kenji Tokitsu's method (Tokitsu Ryu), and the Kajo Tsuboi 's method (Kiryuho), among others.

Hi Allain:

I don't disagree generally with anything you said, however, I'd suggest that the basis to build everything on is to learn how to do Tohei's "Ki Tests". Without those abilities to build on, the "wave" stuff is an external parody, even though the words sound the same. My 2 cents.

An elastic collision preserves the most kinetic energy by conserving all of it.

The best you can do with an elastic collision is for the second ball to leave with double the speed the first ball arrived at -- but this is the theoretical limit as the ratio of the masses approaches infinity.
...
I know *you* know this Mike, more clearly I am sure than I do. I just threw it out there for the number geeks to chew on. If my math's wrong, please point it out -- but I think I got the equations right.

I don't quibble with the math -- I just quibble with the model of the problem. First of all it is even worse than you assume. Because the balls must hit in a spinning collision and here is always some offset in the eccentricity of the collision this results in an amount of the impact energy proportional to the eccentricity of impact being dissipated to increase spin in the target ball -- vice increase linear velocity -- which application of billiard English suitably leads into my main point.

Linear momentum -- p= mv is a proportional system -- mass times velocity, and the kinetic energy increases as half the mass times the square of the velocity 1/2mv^2. -- So only one square term operates in the linear momentum energy equation.

Angular momentum is a very different animal when it comes to concentrating and dissipating kinetic energy, because the inertial radius controls angular velocity, creating an additional effective square term.

Angular momentum (L) -- L = Iω where I is the inertial moment and ω is the angular velocity. Angular velocity is proportional to the inverse of the radius (the skater spins faster when tighter). But the inertial moment of the body also reduces proportional to of the radius, leaving the total angular momentu proportiaonl to the inverse square of the radius.

Thus, by simply reducing the radius of the rotation we add an additional square term to our angular velocity in the kinetic energy equation -- which is the term that is further squared to yield the effective kinetic energy (or by increasing radius to dissipate energy in terms of the inverse square of the radius). This energetic transformation does not operate in in the linear, non-rotational momentum scenario. In in fact as illustrated above induced rotations are a serious source of inefficiency of linear momentum transfer actual collisions. This degree of disproportion in ability to manipulate the energy positively or negatively though rotational transformation cannot be duplicated in linear momentum terms with normal human anatomy.

On the other hand, this rotational energy equation operates at every stage of reducing or increasing effective radius of rotation. You cannot move your body around without every component rotating about its own center as well as about the point of attachment to some other component. Either initially or ultimately it involves rotating the entire length of the body about its center of mass AND its point contact with the earth. (Bishop Berkeley said a pendulum also rotates with reference to the "fixed stars" so the "Ki of Heaven" is actually a bit of a cross- cultural image.)

Commencing a rotation, let's say, of 2 meters radius (exagerrating for simplicity's sake) of my full height and at its center of mass reduced by about 40 percent (Divine proportion) when I lock out the bottom part and then rotate the upper toso about its C.o.M., then again by roughly 40% at every successive limb component, results in a theoretical multiple of about 6.25 times the angular velocity transferred from the immediately prior stage -- at every stage of the progression.

From my whole body to my upper body/shoulder, to my upper arm, to my forearm, to my fist rotating about my wrist -- that is four conversion stages over the initial motion -- so the potential angular velocity delivered is about 6.25 * 6.25 * 6.25 * 6.25 or 6.25^4 = ~ 1500 times the angular velocity -- limited only by inherent inertia, efficiency losses due to asymmetry and the degree of stiffness in the connections. All of these are very large potential inefficiencies, and thus there is a wide field for training to improve on.

The first and second inefficiencies would be addressed by following a spiral symmetry in the whole movement, aligning every part of every limb to the same scheme of rotation -- which is the pattern of Aikido movement. The second inefficiency would be addressed by "softening" the linkages, as Amdur suggests was O Sensei's purpose in adapting the selection of waza for his training regime. That reduces stiffness in rotation for impulse delivery, and also allows increased sensitivity to and coordination of "viscous" coherence of simultaneous joint rotations across the whole body to impulse meant to to be dissipated.

True. You guys have now taken a fairly simple concept and covered it with sequins and flashing lights so that it is not recognizable. Another thread bites the dust, as far as I'm concerned.

Um, sorry about that. Just to be clear, I threw in some quantitative detail to clarify the relatively simple model. I wasn't hoping to make the model much more complex. Some people are naturally going to try to think the details of this through, and and even in a balls-bouncing-off-each-other-linearly model, it's not entirely intuitive what can happen physically. I dropped the analysis in because I had performed it -- for those who actually want to think the *simple* model through completely. It wasn't meant to be an entrée into rotational dynamics (no offense, Eric).

I'd suggest that the basis to build everything on is to learn how to do Tohei's "Ki Tests". Without those abilities to build on, the "wave" stuff is an external parody, even though the words sound the same. My 2 cents.

Holy Cow! You guys are amazing. No, I really mean it. I just know how to do the motion but I am amazed at the explanations you are all going through. Keep it up but I have to tell you I have a Ph.D. in social work so I just know how I feel about the discussion, but I am not sure I understand it all. You passed my physics understanding a couple of "undulations" ago. But pleae, keep chatting, it is very interesting.

You gotta be kidding me. This sort of rant belongs on alt.physics.boredomcoma.lookatme.lookatme. Can we get back to martial arts please?

An honest question. But what do you imagine martial art is? If you cannot reliably disassemble the rifle and reassemble the rifle, understand the components of its operation that are likely to foul, bend, break and need cleaning or replacement (burnishing our arms and our training is the constant work of the warrior) -- you have no business bearing that rifle in a combat situation. In which case -- more training and more understanding is necessary.

One may choose to study one aspect of warfare more intensively than another. But dismissing any area of relevant knowledge is simply unwise. Any misunderstood detail or principle of action can literally mean life or death. Martial art therefore admits of no aspect of the understanding of its action that is not worthy of intensive study. Anything less is just performance art.

Someone starts a thread on "Wave motion theory" and angular momentum intrinsically applies to that discussion and I bring that discussion to the table. I do not have to justify my approach. I did not invent the idea of this path -- the Founder himself did. Argue with him, not me. And good luck with that.

Quote:

O Sensei - Budo wrote:

If he comes with ki, strike with ki; if he comes with water, strike with water; if he comes with fire, strike with fire. Think about such things and their relationship to modern scientific warfare when you train.

Quote:

O Sensei wrote:

The Aiki Path is infinite. ...In Aikido you must understand every phenomenon in the universe. For example, the rotation of the Earth and the most intricate and far-reaching system of the universe. ... The technique of Aiki is ascetic training and a way through which you reach a state of unification of body and spirit by the realization of the principle of heaven.

While there may be others, there is at least one physical concept that is in operation everywhere from the farthest limits of observation at the farthest reaches of the universe to the infinitesimal limits of the Planck scale -- it is angular momentum. It is conserved in exceedingly mysterious and counterintuitive ways, even in the understanding of modern science, and even such as Newton got it wrong in a fairly fundamental way, even in classical terms. You may not chose to study things in this way, and more power to you, but, as I said, I was not the first to go technical in this discussion.

Tim, that looks like a karate-type form that Hiroo Sensei must have created. It seems to have elements similar to sanchin and tensho, but, obviously, is neither of those. This was not included in Minoru Sensei's yoseikan. His katas (except happo ken) all resembled traditional judo and jujutsu forms. Since Hiroo is a master of wado ryu (and, I think, some other karate styles), his approach seems much more strongly influenced by karate and this form looks to me like something he developed, himself.

As to whether it's typical solo training for yoseikan budo, I'd have to say, from my encounters with Hiroo Sensei's system, it looks pretty typical.

Hope that helps.

Best to you.

David

"That which has no substance can enter where there is no room."
Lao Tzu